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dc.contributor.authorLang, Jérôme Michel 14:36:32 (GMT) 14:36:32 (GMT)
dc.description.abstractIt has been conjectured that general relativistic shear-free perfect fluids with a barotropic equation of state, and such that the energy density, µ, and the pressure, p, satisfy µ + p ̸= 0, cannot simultaneously be rotating and expanding (or contracting). A survey of the known results about this conjecture is included herein. We show that the conjecture holds true under either of the following supplementary conditions: 1) the Weyl tensor is purely magnetic with respect to the flow velocity vector or 2) dp/dµ = −1/3. Any hypersurface-homogeneous shear-free perfect fluid which is not space-time homogeneous and whose acceleration vector is not parallel to the vorticity vector belongs to one of three invariantly defined classes, labelled A, B and C. It is found that the Petrov types which are allowed in each class are as follows: for class A, type I only; for class B, types I, II and III; and for class C, types I, D, II and N. Two-dimensional pseudo-Riemannian space-times are classified in a manner similar to that of the Karlhede classification of four-dimensional general-relativistic space-times. In an appendix, the forms differential forms package for the Maple program is described.en
dc.publisherUniversity of Waterlooen
dc.subjectGeneral Relativityen
dc.subjectEquivalence Methoden
dc.subjectShear-free conjectureen
dc.subjectDifferential forms Maple packageen
dc.titleContributions to the study of general relativistic shear-free perfect fluids: an approach involving Cartan's equivalence method, differential forms and symbolic computationen
dc.typeDoctoral Thesisen
dc.pendingfalse Mathematicsen Mathematicsen of Waterlooen
uws-etd.degreeDoctor of Philosophyen
uws.contributor.advisorCollins, Christopher Barry
uws.contributor.affiliation1Faculty of Mathematicsen

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